Extensions 1→N→G→Q→1 with N=C₁₀ and Q=GL₂(𝔽₃)

Direct product G=N×Q with N=C₁₀ and Q=GL₂(𝔽₃)

		d	ρ	Label	ID
C₁₀×GL₂(𝔽₃)		80		C10xGL(2,3)	480,1017

Semidirect products G=N:Q with N=C₁₀ and Q=GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊GL₂(𝔽₃) = C₂×Q₈⋊D₁₅	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₁₀	80		C10:GL(2,3)	480,1028

Non-split extensions G=N.Q with N=C₁₀ and Q=GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.GL₂(𝔽₃) = Q₈⋊Dic₁₅	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₁₀	160		C10.GL(2,3)	480,260
C₁₀.₂GL₂(𝔽₃) = C₅×Q₈⋊Dic₃	central extension (φ=1)	160		C10.2GL(2,3)	480,256

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Extensions 1→N→G→Q→1 with N=C10 and Q=GL2(𝔽3)